Compressible mixing layer in shock-induced separation

Abstract

Unsteadiness in separated shock–boundary layer interactions have been previously analysed in order to propose a scenario of entrainment–discharge as the origin of unsteadiness. It was assumed that the fluid in the separated zone is entrained by the free shear layer formed at its edge, and that this layer follows the properties of the canonical mixing layer. This last point is addressed by reanalysing the velocity measurements in an oblique shock reflection at a nominal Mach number of 2.3 and for two cases of flow deviation ($8^{\circ }$ and $9.5^{\circ }$). The rate of spatial growth of this layer is evaluated from the spatial growth of the turbulent stress profiles. Moreover, the entrainment velocity at the edge of the layer is determined from the mean velocity profiles. It is shown that the values of turbulent shear stress, spreading rate and entrainment velocity are consistent, and that they follow the classical laws for turbulent transport in compressible shear layers. Moreover, the measurements suggest that the vertical normal stress is sensitive to compressibility, so that the anisotropy of turbulence is affected by high Mach numbers. Dimensional considerations proposed by Brown & Roshko (J. Fluid Mech., vol. 64, 1974, 775–781) are reformulated to explain this observed trend.

On the turbulence amplification in shock-wave/turbulent boundary layer interaction

“…The peak is defined as the local maximum along the wall-normal direction at an x-station. The main characteristic is the amplification of all the Reynolds stress components with their peaks moving from the near-wall region to the core of the free shear layer or mixing layer, which has been reported previously (Dupont et al 2005(Dupont et al , 2006(Dupont et al , 2008(Dupont et al , 2019Pirozzoli & Grasso 2006;Wu & Martín 2007;Li et al 2010;Priebe & Martín 2012;Helm et al 2014) as evidence of the turbulence amplification mechanism due to the free shear layer.…”

“…Indeed, several research articles have reported high turbulence intensity in the near-wall region close to the foot of the reflected shock wave both experimentally (Dupont et al 2008) and numerically (Wu & Martín 2007;Li et al 2010). Two separated turbulence kinetic energy maxima in the near-wall region and outer part of the boundary layer were also observed (Dupont et al 2005(Dupont et al , 2006(Dupont et al , 2019. The new turbulence amplification mechanism proposed in the present paper will provide a clear physical explanation for these observations.…”

“…Further downstream, the value of u u peak is doubled at x = −2.02, and its peak is still in the inner region of the boundary layer ( y peak = 0.02δ ref ), and the global maximum of u u is achieved at x = −1.76 with its wall-normal position at y peak = 0.04δ ref , where u u is amplified by 140 %. The near-wall peak of Reynolds stress was also observed in the experiment of Dupont et al (2005), Dupont et al (2006), Dupont et al (2008) and Dupont et al (2019), and therefore we suspect that the amplification of turbulence, at least for u u , may not be due to the free shear layer detached from the mean separation position.…”

“…They also reported that the velocity profile in the detached free shear layer was similar to the mixing layer and attributed the strong turbulence in the free shear layer to a Kelvin-Helmholtz (K-H) instability. The detached free shear layer in SWTBLI is then further confirmed to be essentially a compressible mixing layer (Dupont et al 2019).…”

“…Andreopoulos, Agui & Briassulis (2000) reviewed various kinds of shock-wave/turbulence interactions, and they argued that the turbulence amplification was not only affected by the shock interaction, but also by the unsteadiness of the shock system, the destabilising effect of the concave streamline curvature and the On the turbulence amplification in SWTBLI 897 A32-3 continuing downstream compression. In the recent measurements in OSWFPBLIs of Dupont et al (2005), Dupont, Haddad & Debiève (2006) and Dupont, Piponniau & Dussauge (2019), two separated maxima of amplified turbulence, especially for the streamwise velocity fluctuations, were identified. The first maximum is in the near-wall region immediately downstream of the reflected shock wave, and the second is away from the wall and preserved far downstream of the reattachment point.…”